Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #2984 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D7 |
| commutator, socle | C22×C7 | C23×C4 |
| Fitting | C7×#432 | C2 |
| prime radical | C23×C7 | C22×C4 |
| cosocle | C2×C4×C7 | C24 |
| hypercenter | #432 | D7 |
| hypocenter | C7 | #2984 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ #432 | |
364 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,h^a=h^6,c^b=ceg,h^b=h^6134 conjugacy classes — view the full character table.
| maximal subgroup of | #13249623, #13249627, #13249637, … |
| maximal normal subgroup of | #13249623, #13249627, #13249637, … |
| maximal quotient of | #13352539, #13352540, #13352857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11526);